Fibring of Logics as a Universal Construction

1 PROLEGOMENON TO FIBRING It is a task of philosophy to explain the sense in which contemporary science uses the label " logics " , specially through " logics in " (natural language, program verification, machine learning, knowledge representation, abduc-tive and inductive reasoning, etc.) as well as " logics for " (hybrid reasoning systems, ontology, engineering, reasoning about cryptographic construction, defeasible argumentation, reasoning with uncertainty, reasoning under contradiction , reasoning about action, agents with bounded rationality, and so on) and even " logics that " (that characterize classes of finite structures as in finite model theory, that characterize formal grammars, that characterize processes, etc.) The Greek term logos (and ratio in Latin) from which " logic " and " reason " derive, with its original meaning of " to put together " , and later " to speak about " is suggestive: it may be relevant for such domains to start by collecting peculiar concepts and thoughts, and then recompiling them in an orderly way using logical tools so that talking and reasoning about the resulting concepts becomes something practical and effective. Whether or not such usage favours logical pluralism (in the sense that there is more than one " real logic " ') or just reflects isolated parts of the conception of reason as cosmic ordering, is also a matter for philosophy, as it is also to reconcile this practice with logic regarded as an epistemological enterprise or to Kant's transcendental deduction. But what is more: the contemporary usage of the term logic specializes from the formal logic (in the sense of abiding to the criteria of concept, judgment, and inference) not only towards using symbolic logic (i.e., a development of formal logic by means of mathematical concepts), but also by means of mechanized, computer-based concepts, or in other words, by means of the algorithmic side of logic. It is natural to think that the intense use of " logics in " , " logics that " and even " logics " with no specifications can be combined again by mathematical methods, realizing a certain philosophers and logicians dream to building mechanisms where several different logics could interact and cooperate , instead of clashing. In this sense the project of reducing reasoning to symbolic computation is an old one. The philosopher and mathematician Bernard Bolzano born in Prague, Bohemia was not far from proposing the